I'm not sure if any of this was discussed before, I checked a bit, but I'm pretty lazy...
Ok, here we go. Isn't it strange that most powerful wizard, well, second, is a halfblood? (Lord Voldemort). Also, Harry is pretty powerful for an underage wizard, and he is also a halfblood. While Ron and Neville, though they are both pretty talented (or getting there), are purebloods and are at no means, the same level as Harry when it comes to magic. Then there are the muggleborns like Hermione and Lily. In classes, Hermione is the first to learn new spells, all the time. Lily, who's wand was good for charms, I guess you can assume she was along the same lines- especially since she ended up as Head Girl.
My first point is that, halfbloods seem to be much more powerful than any other wizard, which got me down the path to thinking that Dumbledore could very possibly be a halfblood. Not that I think he's the HBP, it would just be interesting to see if blood really effects how good of a wizard you are.
Next point, doens't Hermione remind you of Lily in some ways? Could it be they're heading down the same path? It's pretty obvious that Hermione is Head Girl material, and I don't know if we ever find out what Hermione's wand is, but wouldn't it be cool if it were similiar to Lily's? Maybe that's why people think that Hermione and Harry have a 'thing', because she's rather like a mother, don't you think? The way she thinks ahead is not a teenage characteristic. Then in OotP, Hermione is taken out of the battle in the MoM, could this be foreshadowing that Hermione might not live?